This far, this fast, using pre-knowlege of floor layout and contents (force-quit / restart method). I suggested this method somewhere else in the forums as the ultimate in cheating, wanted to see just how well it would work. Gave up on a full run (pit trap basically killed the attempt; I didn't have a ring of searching or disarming), but... pretty far. Had I pressed on I might have been able to finish a full amulet retrieval in under 5K turns with a non-secret character. Used CHEATER as character name to make it very clear that this run wasn't on the up-and-up.